Finite Group Databasebeta

← D43×#1579 #25065986

Subgroups — D43×#1579 #25065986

Order 11008.

718 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×Q8×D43C212yesmaximal
2C4×Q16×D43C211yesmaximal, characteristic
3#19133415C211yesmaximal, characteristic, complemented
4#19133414C211yesmaximal, characteristic, complemented
5#19133413C211yesmaximal, characteristic, complemented
6#19133412C212yesmaximal, complemented
7#19133411C212yesmaximal, complemented
8#334×D43C211yesmaximal, characteristic
9Q8⋊C8×D43C212yesmaximal
10#322×D43C211yesmaximal, characteristic
11C43×#1579C211yesmaximal, characteristic, complemented
12C2×Q16×D43C411yescharacteristic
13C4×Q8×D43C2212yes—
14Q8×C43⋊C8C2212yes—
15C8×Dic86—22no—
16C8×Dic86C2212yes—
17#14583023—22no—
18#14583023C2212yes—
19C4×Dic172C2211yescharacteristic
20Q16×Dic43C411yescharacteristic
21#14582993C411yescharacteristic
22C4×#10621885C2212yes—
23#14582991C412yes—
24#107×D43C411yescharacteristic
25C4⋊C8×D43—22no—
26C4⋊C8×D43C2212yes—
27#103×D43C412yes—
28C4×C8×D43—22no—
29C4×C8×D43C2211yescharacteristic
30C4×C8×D43C2211yescharacteristic
31C4×C8×D43C2211yescharacteristic
32#14582650C2211yescharacteristic
33#14582649C2212yes—
34#14582631C2212yes—
35Q8⋊(C43⋊C8)C2212yes—
36#14582629C2212yes—
37#14582621C2211yescharacteristic
38#14582621C2211yescharacteristic
39#14582620C2211yescharacteristic
40C8×Q8×C43C2212yes—
41C4×Q16×C43C2211yescharacteristic
42C43×#334C2211yescharacteristic
43C43×Q8⋊C8C2212yes—
44C43×#322C2211yescharacteristic
45C2×Q8×D43C2×C412yes—
46C2×Dic172C2×C411yescharacteristic
47C2×#10621885C2×C412yes—
48Q16×D43C818yescomplemented
49C2×C8×D43—22no—
50C2×C8×D43—21no—
51C2×C8×D43C2×C411yescharacteristic
52C2×C8×D43C2×C411yescharacteristic
53C2×C8×D43D412yes—
54Q8×Dic43C2×C412yes—
55C4×Dic86—22no—
56C4×Dic86C2312yes—
57#13063290—22no—
58#13063290C2×C412yes—
59C4⋊C4×D43—22no—
60C4⋊C4×D43C2×C412yes—
61C42×D43—22no—
62C42×D43C2311yescharacteristic
63#13063259C2×C411yescharacteristic
64#13063258C2×C412yes—
65C4⋊(C43⋊C8)—22no—
66C4⋊(C43⋊C8)C2312yes—
67Dic43⋊C8—22no—
68Dic43⋊C8—22no—
69Dic43⋊C8—22no—
70#13063250C2×C412yes—
71#13063249C2×C412yes—
72#13063248C2×C412yes—
73C4×C43⋊C8—22no—
74C4×C43⋊C8C2311yescharacteristic
75C4×C43⋊C8C2311yescharacteristic
76C4×C43⋊C8C2311yescharacteristic
77C8×Dic43—22no—
78C8×Dic43—21no—
79C8×Dic43—22no—
80C8×Dic43C2×C411yescharacteristic
81C8×Dic43C2×C411yescharacteristic
82C8×Dic43D412yes—
83C2×Q16×C43C2×C411yescharacteristic
84C4×Q8×C43C2312yes—
85#107×C43C2×C411yescharacteristic
86C4⋊C8×C43—22no—
87C4⋊C8×C43C2312yes—
88#103×C43C2×C412yes—
89C4×C8×C43—22no—
90C4×C8×C43C2311yescharacteristic
91C4×C8×C43C2311yescharacteristic
92C4×C8×C43C2311yescharacteristic
93C2×Q8×C43C22×C412yes—
94Q8×D43—24no—
95Q8×D43C2×C818yes—
96C2×C4×D43—22no—
97C2×C4×D43—22no—
98C2×C4×D43C22×C411yescharacteristic
99C2×C4×D43C2×D411yescharacteristic
100C2×C4×D43#4111yescharacteristic
101C2×Dic86—22no—
102C2×Dic86C22×C412yes—
103Q16×C43C2×C814yescomplemented
104C2×C8×C43—22no—
105C2×C8×C43—21no—
106C2×C8×C43C22×C411yescharacteristic
107C2×C8×C43C22×C411yescharacteristic
108C2×C8×C43C2×D412yes—
109C4⋊C4×C43—22no—
110C4⋊C4×C43C22×C412yes—
111C42×C43—22no—
112C42×C43C2411yescharacteristic
113#10621885C2×C818yescomplemented
114C4⋊Dic43—22no—
115C4⋊Dic43C22×C412yes—
116Dic43⋊C4—22no—
117Dic43⋊C4—22no—
118Dic43⋊C4—22no—
119C4×Dic43—22no—
120C4×Dic43—22no—
121C4×Dic43—22no—
122C4×Dic43C22×C411yescharacteristic
123C4×Dic43C2×D411yescharacteristic
124C4×Dic43#4111yescharacteristic
125C2×C43⋊C8—22no—
126C2×C43⋊C8—21no—
127C2×C43⋊C8C22×C411yescharacteristic
128C2×C43⋊C8C22×C411yescharacteristic
129C2×C43⋊C8C2×D412yes—
130Dic172C2×C814yescomplemented
131C8×D43—22no—
132C8×D43—24no—
133C8×D43—42no—
134C8×D43—44no—
135C8×D43C2×C814yes—
136C22×D43C4×D411yescharacteristic
137Q8×C43—22no—
138Q8×C43C22×C814yes—
139C2×C4×C43—22no—
140C2×C4×C43—22no—
141C2×C4×C43C23×C411yescharacteristic
142C2×C4×C43C22×D411yescharacteristic
143C2×C4×C43C2×#4111yescharacteristic
144C2×Dic43—22no—
145C2×Dic43—22no—
146C2×Dic43C4×D411yescharacteristic
147C2×Dic43C4×D411yescharacteristic
148C2×Dic43C4×D411yescharacteristic
149C4×D43—28no—
150C4×D43—22no—
151C4×D43—44no—
152C4×D43C22×C812yes—
153C4×D43#13112yes—
154C4×D43#13714yes—
155Dic86—22no—
156Dic86—28no—
157Dic86C22×C814yes—
158C8×C43—21no—
159C8×C43—22no—
160C8×C43—41no—
161C8×C43—42no—
162C8×C43C22×C812yes—
163C43⋊C8—21no—
164C43⋊C8—22no—
165C43⋊C8—41no—
166C43⋊C8—42no—
167C43⋊C8C22×C812yes—
168C2×#1579—431nomaximal, Sylow
169C22×C43C2×C4×D411yescharacteristic
170C2×D43C8×D412yes—
171C2×D43#44112yes—
172C2×D43#44412yes—
173C4×C43—24no—
174C4×C43—21no—
175C4×C43—42no—
176C4×C43C23×C811yescharacteristic
177C4×C43C2×#13111yescharacteristic
178C4×C43C2×#13712yes—
179Dic43—24no—
180Dic43—21no—
181Dic43—42no—
182Dic43C8×D412yes—
183Dic43#44112yes—
184C2×C8×Q8—432no—
185C2×C4×Q16—431no—
186#1579—432no—
187#1579—431no—
188#1579—431no—
189#1579—432no—
190#1579—431no—
191#1579D4311yescharacteristic, direct product factor
192C2×#334—431no—
193C2×Q8⋊C8—432no—
194C2×#322—431no—
195C2×C43C2×C8×D411yescharacteristic
196C2×C43C2×#44111yescharacteristic
197C2×C43C2×#44411yescharacteristic
198D43#157914yesdirect product factor
199C22×Q16—431no—
200C2×C4×Q8—432no—
201C8×Q8—432no—
202C8×Q8—432no—
203C8×Q8—432no—
204C8×Q8—862no—
205C8×Q8—862no—
206C8×Q8C2×D4312yes—
207C4×Q16—431no—
208C4×Q16—432no—
209C4×Q16—431no—
210C4×Q16—432no—
211C4×Q16—431no—
212C4×Q16C2×D4311yescharacteristic
213C2×#107—431no—
214C2×C4⋊C8—432no—
215C2×C4⋊C8—862no—
216C2×#103—432no—
217C2×C4×C8—431no—
218C2×C4×C8—431no—
219C2×C4×C8—431no—
220C2×C4×C8—862no—
221#334—432no—
222#334—431no—
223#334C2×D4311yescharacteristic
224Q8⋊C8—432no—
225Q8⋊C8—432no—
226Q8⋊C8—432no—
227Q8⋊C8C2×D4312yes—
228#322—431no—
229#322—431no—
230#322—431no—
231#322C2×D4311yescharacteristic
232C43C2×#157911yescharacteristic, complemented, Sylow
233C22×Q8—432no—
234C2×Q16—432no—
235C2×Q16—438no—
236C2×Q16—431no—
237C2×Q16C4×D4311yescharacteristic
238C22×C8—431no—
239C22×C8—431no—
240C22×C8—432no—
241C22×C8—861no—
242C22×C8—862no—
243C4×Q8—432no—
244C4×Q8—432no—
245C4×Q8—432no—
246C4×Q8—862no—
247C4×Q8—862no—
248C4×Q8C22×D4312yes—
249C2×C4⋊C4—432no—
250C2×C4⋊C4—862no—
251C2×C42—431no—
252C2×C42—862no—
253#107—431no—
254#107—432no—
255#107C4×D4311yescharacteristic
256C4⋊C8—22no—
257C4⋊C8—432no—
258C4⋊C8—862no—
259C4⋊C8—862no—
260C4⋊C8—862no—
261C4⋊C8—862no—
262C4⋊C8C22×D4312yes—
263#103—432no—
264#103—432no—
265#103—432no—
266#103C4×D4312yes—
267C4×C8—22no—
268C4×C8—431no—
269C4×C8—431no—
270C4×C8—432no—
271C4×C8—431no—
272C4×C8—431no—
273C4×C8—431no—
274C4×C8—862no—
275C4×C8—861no—
276C4×C8—862no—
277C4×C8—862no—
278C4×C8C22×D4311yescharacteristic
279C4×C8C22×D4311yescharacteristic
280C4×C8C22×D4311yescharacteristic
281C2×Q8—438no—
282C2×Q8—432no—
283C2×Q8—862no—
284C2×Q8—864no—
285C2×Q8C2×C4×D4312yes—
286C22×C4—431no—
287C22×C4—431no—
288C22×C4—431no—
289C22×C4—862no—
290C22×C4—862no—
291Q16—438no—
292Q16—434no—
293Q16C8×D4314yescomplemented
294C2×C8—22no—
295C2×C8—21no—
296C2×C8—431no—
297C2×C8—434no—
298C2×C8—431no—
299C2×C8—432no—
300C2×C8—862no—
301C2×C8—864no—
302C2×C8—862no—
303C2×C8—861no—
304C2×C8—1724no—
305C2×C8—1722no—
306C2×C8C2×C4×D4311yescharacteristic
307C2×C8C2×C4×D4311yescharacteristic
308C2×C8D4×D4312yes—
309C4⋊C4—22no—
310C4⋊C4—432no—
311C4⋊C4—862no—
312C4⋊C4—862no—
313C4⋊C4—862no—
314C4⋊C4—862no—
315C4⋊C4C2×C4×D4312yes—
316C42—22no—
317C42—431no—
318C42—431no—
319C42—431no—
320C42—862no—
321C42—862no—
322C42—862no—
323C42C23×D4311yescharacteristic
324C23—431no—
325Q8—22no—
326Q8—434no—
327Q8—868no—
328Q8—862no—
329Q8C2×C8×D4314yes—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—431no—
333C2×C4—431no—
334C2×C4—432no—
335C2×C4—432no—
336C2×C4—434no—
337C2×C4—431no—
338C2×C4—862no—
339C2×C4—868no—
340C2×C4—862no—
341C2×C4—862no—
342C2×C4—1724no—
343C2×C4C22×C4×D4311yescharacteristic
344C2×C4C2×D4×D4311yescharacteristic
345C2×C4#41×D4311yescharacteristic
346C8—21no—
347C8—22no—
348C8—41no—
349C8—42no—
350C8—432no—
351C8—861no—
352C8—862no—
353C8—1721no—
354C8—1722no—
355C8C2×C8×D4312yes—
356C22—432no—
357C22—432no—
358C22—432no—
359C22C4×D4×D4311yescharacteristic
360C4—21no—
361C4—24no—
362C4—42no—
363C4—432no—
364C4—432no—
365C4—861no—
366C4—864no—
367C4—1722no—
368C4C22×C8×D4311yescharacteristic
369C4#131×D4311yescharacteristic
370C4#137×D4312yes—
371C2—434no—
372C2C8×D4×D4311yescharacteristic
373C2#441×D4311yescharacteristic
374C2#444×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC4×C43C23×C8
FrattiniC42C23×D43
FittingC43×#1579C2
socleC22×C43C2×C4×D4
prime radicalC22×D43C4×D4
cosocleC42×C43C24
hypercenter#1579D43
hypocenterC43C2×#1579
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1579

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #19133415C2semidirect
4. #19133414C2semidirect
5. #19133413C2semidirect
6. #19133412C2semidirect
7. #19133411C2semidirect
11. C43×#1579C2semidirect
48. Q16×D43C8semidirect
103. Q16×C43C2×C8semidirect
113. #10621885C2×C8semidirect
130. Dic172C2×C8semidirect
191. #1579D43direct (N × H)
198. D43#1579direct (N × H)
232. C43C2×#1579semidirect
293. Q16C8×D43semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C8×Q8×D432
C4×Q16×D432
#191334152
#191334142
#191334132
#191334122
#191334112
#334×D432
Q8⋊C8×D432
#322×D432
C43×#15792
C2×#157943